Displaying similar documents to “Combinatorial homology in a perspective of image analysis.”

Effective homology for homotopy colimit and cofibrant replacement

Marek Filakovský (2014)

Archivum Mathematicum

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We extend the notion of simplicial set with effective homology presented in [22] to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets X : ℐ → sSet such that each simplicial set X ( i ) has effective homology, we present an algorithm computing the homotopy colimit hocolim X as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement X cof of X as a diagram with effective homology. This is applied to computing of equivariant cohomology...

Topos based homology theory

M. V. Mielke (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects....

Homotopy Invariance of Transverse Homology Functors

Sara Dragotti, Gaetano Magro, Lucio Parlato (2007)

Bollettino dell'Unione Matematica Italiana

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We construct, here, transverse homology functors, and we prove their invariance with respect to a suitable definition of homotopy.

A 2-category of chronological cobordisms and odd Khovanov homology

Krzysztof K. Putyra (2014)

Banach Center Publications

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We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms along any 3-dimensional subcube is trivial. This allows us to create a chain complex whose homotopy type modulo certain relations is a link invariant. Both the original and...